I do still need to program in shell script from time to time

I tend to forget how to increment a variable

There are several ways:

var=$((var+1))
((var+=1))
((var++))
let “var=var+1”

Usage of the double parenthesis explained:

http://tldp.org/LDP/abs/html/dblparens.html

A good place to learn about shell script in bash:
http://www.tutorialspoint.com/unix/unix-using-variables.htm